526. Beautiful Arrangement

Suppose you have N integers from 1 to N. We define a beautiful arrangement as an array that is constructed by these N numbers successfully if one of the following is true for the ith position (1 <= i <= N) in this array:

The number at the ith position is divisible by i.
i is divisible by the number at the ith position.

Now given N, how many beautiful arrangements can you construct?

Example 1:

Input: 2

Output: 2

Explanation: 

The first beautiful arrangement is [1, 2]:

Number at the 1st position (i=1) is 1, and 1 is divisible by i (i=1).

Number at the 2nd position (i=2) is 2, and 2 is divisible by i (i=2).

The second beautiful arrangement is [2, 1]:

Number at the 1st position (i=1) is 2, and 2 is divisible by i (i=1).

Number at the 2nd position (i=2) is 1, and i (i=2) is divisible by 1.

Note:

N is a positive integer and will not exceed 15.

Approach #1: backtracking. [C++]

class Solution {

public:

    int countArrangement(int N) {

        vector<int> path;

        for (int i = 1; i <= N; ++i)

            path.push_back(i);

        return helper(N, path);

    }

private:

    int helper(int n, vector<int> path) {

        if (n <= 0) return 1;

        int ans = 0;

        for (int i = 0; i < n; ++i) {

            if (path[i] % n == 0 || n % path[i] == 0) {

                swap(path[i], path[n-1]);

                ans += helper(n-1, path);

                swap(path[i], path[n-1]);

            }

        }

        return ans;

    }

};

巴特西

526. Beautiful Arrangement

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